Let \(Q_{n,k}\) be an enhanced hypercube, which is an variant of the well-known hypercube \(Q_n\) and is constructed from \(Q_n\) by adding \(2^{n-1}\) complementary edges. A network G is said to be under the conditional fault model if every fault-free vertex of G is incident to at least two fault-free edges. Let \(F_v\) and \(F_e\) be the set of faulty vertices and faulty edges in \(Q_{n,k}~(1\le k\le n-1)\) , respectively. In this paper, under the conditional fault model, we prove that \(Q_{n,k}-F_v-F_e\) contains a fault-free cycle of every even length l with \(4\le l\le 2^n-2|F_v|\) when \(|F_v|+|F_e|\le 2n-4\) and \(n\ge 3\) .
